Cylinder Surface Area and Volume: Keeping Formulas Straight

Memorizing formulas has always been confusing business for me.  If all I know about an operation or problem is the formula than it becomes nearly impossible to remember.  What I'm getting at is this: once I understand what the formula is doing to the numbers and why, I won't forget it.  This isn't just the way my brain works, but this describes how I retain information most effectively.  I remember something best if I dissect it and see how it works.  Once I understand how it works, it's easily woven into memory.

Sometimes while calculating the surface area and volume of a cylinder I found myself unsure which formula I should use...

The two formulas I would get confused and accidentally interchange were the formulas for circumference and area of a circle.



To calculate the circumference we are multiplying the diameter by that special irrational number describes the relationship between the circumference of a circle and the diameter.


Another way to remember which formula to use it to examine the units of the answer.  If the answer needed is area than it must use the formula that produces an answer in two dimensions or squared units.  Similarly, if the answer is a volume you must use the formula that produces an answer in 3 dimensions, or cubed units.  Keeping the units accurate throughout the process of a multi step solution can save the solver tons of headache and confusion.